Approximation numbers = singular values

• This paper introduces a generalisation of the notion of singular value for Hilbert space operators to more general Banach spaces. It is shown that for a simple integral operator of Hardy type the singular values are the eigenvalues of a non-linear Sturm-Liouville equation and coincide with the approximation numbers of the operator. Finally, asymptotic formulas for the singular numbers are deduced. (c) 2006 Published by Elsevier B.V.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Pruefer transform

eigenvalue

generalised trigonometric function

asymptotics

Bernstein width

Sturm-Liouville

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)